Depending on the nick, an old trick is to cut the excess off (from the nick) wet the raw leather underneath, and press it under a book until it dries. The porous leather beneath will at first swell up to meet the level of the book (and the rest of the strop) and then, as it dries, harden that way. It will be a little different, but much better than the original nick. You can then use a pumice stone or conditioner or whatever treatment you feel like, followed by a good rubbing with a glass bottle to smooth it out.
Hope this helps.

John P.